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Local structure change evidenced by temperature-dependent elastic measurements:Case study on Bi1/2Na1/2TiO3-based lead-free relaxor piezoceramicsRobert Dittmer, Wook Jo, Kyle G. Webber, Jacob L. Jones, and Jürgen Rödel Citation: Journal of Applied Physics 115, 084108 (2014); doi: 10.1063/1.4866092 View online: http://dx.doi.org/10.1063/1.4866092 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Long ranged structural modulation in the pre-morphotropic phase boundary cubic-like state of the lead-freepiezoelectric Na1/2Bi1/2TiO3-BaTiO3 J. Appl. Phys. 114, 234102 (2013); 10.1063/1.4842855 Phase transitions, relaxor behavior, and large strain response in LiNbO3-modified Bi0.5(Na0.80K0.20)0.5TiO3lead-free piezoceramics J. Appl. Phys. 114, 044103 (2013); 10.1063/1.4816047 Quenching-induced circumvention of integrated aging effect of relaxor lead lanthanum zirconate titanate and(Bi1/2Na1/2)TiO3-BaTiO3 Appl. Phys. Lett. 102, 032901 (2013); 10.1063/1.4788932 Electric-field-induced and spontaneous relaxor-ferroelectric phase transitions in (Na1/2Bi1/2)1−xBaxTiO3 J. Appl. Phys. 112, 124106 (2012); 10.1063/1.4770326 Frequency-dependence of large-signal properties in lead-free piezoceramics J. Appl. Phys. 112, 014101 (2012); 10.1063/1.4730600
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Local structure change evidenced by temperature-dependent elasticmeasurements: Case study on Bi1/2Na1/2TiO3-based lead-free relaxorpiezoceramics
Robert Dittmer,1 Wook Jo,1,a) Kyle G. Webber,1 Jacob L. Jones,2 and J€urgen R€odel11Institute of Materials Science, Technische Universit€at Darmstadt, Alarich-Weiss-Str. 2, 64287 Darmstadt,Germany2Materials Science and Engineering, University of Florida, 135A Rhines Hall, Gainesville, Florida32611-6400, USA
(Received 11 December 2013; accepted 5 February 2014; published online 26 February 2014)
The temperature-dependent Young’s modulus Y(T) of the lead-free piezoceramics of
0.8Bi1/2Na1/2TiO3-0.2Bi1/2K1/2TiO3 (20BKT) and 0.96(0.8Bi1/2Na1/2TiO3-0.2Bi1/2K1/2TiO3)-0.04
BiZn1/2Ti1/2O3 (4BZT) is measured with the impulse excitation technique and contrasted with
corresponding dielectric and structural data. While the dielectric properties suggest a phase
transition, the high resolution XRD patterns remain virtually unchanged from room temperature up
to high temperatures, confirming no change in their long-range order. In contrast, the elastic
properties indicate a broad and diffuse ferroelastic transition denoted by a minimum in Y(T). By
analogy to the elastic and dielectric data of PbZrxTi1�xO3 and PLZT, it is concluded that 20BKT
and 4BZT are relaxors with polar nanoregions embedded in a metrically cubic matrix.
Interestingly, no indication for the freezing temperature was reflected in any of the employed
measurement techniques. From the saturation of Y(T), it is suggested that the Burns temperature
may be approximated as 700 �C. Moreover, it is found that the modification with the ternary
end-member BiZn1/2Ti1/2O3 results in an increase in Young’s modulus. A comparison with the
Bi1/2Na1/2TiO3-BaTiO3-K0.5Na0.5NbO3 yields the same results. VC 2014 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4866092]
I. INTRODUCTION
Piezoceramics based on bismuth sodium titanate1
Bi1/2Na1/2TiO3 (BNT) have attracted considerable attention
in the search for lead-free alternatives to the ubiquitous lead
zirconate titanate PbZrxTi1�xO3 (PZT).2,3 Pseudobinary
solid solutions with BaTiO3 (BT) or Bi1/2K1/2TiO3 (BKT)
were shown to exhibit peculiar features like a field-induced
phase transition4,5 and a frequency-dispersive local maxi-
mum in the temperature-dependent permittivity.6,7 Chemical
modifications afford to tailor the properties for specific appli-
cations. For example, incorporation of K0.5Na0.5NbO3
(KNN),8 SrTiO3 (ST),9 BiAlO3 (BA),10 or BiZn1/2Ti1/2O3
(BZT)11 allows for large field-induced strains, the origin of
which was recently identified as incipient piezoelectric-
ity,12,13 or nearly temperature-insensitive permittivity for
high-temperature capacitors.14
The crystal structure and its thermal evolution are still
under debate for many BNT-based systems.3,15 High-
temperature diffraction studies have so far not provided a
conclusive explanation for the features observed in the high-
temperature permittivity measurements possibly due to the
inherent resolution limit of the diffraction techniques.16 In
other words, the entities responsible for the observed electri-
cal properties, e.g., polar nanoregions (PNRs) are too small
to be resolved by conventional diffraction techniques.
BNT-based materials have been suggested to be relaxor
ferroelectrics that feature PNRs embedded in a metrically
cubic phase.17,18 With sizes typically below 10 nm, these
PNRs fall below the correlation length of X-ray and neutron
diffraction experiments, and are, therefore, hard to detect.
Consequently, the diffraction patterns appear metrically
cubic with a strongly diffuse background.
Measurement of the temperature-dependent elastic prop-
erties provides a powerful tool to monitor temperature-driven
processes. Hence, it offers a natural pathway to detect phase
transitions as Y(T) depends on the interatomic or ionic bond-
ing strength. For example, the sequence of three phase transi-
tions in barium titanate is clearly reflected in changes of the
Young’s modulus.19 At the paraelectric (PE) to ferroelectric
(FE) transition at �130 �C, the Young’s modulus decreases
by almost 50% within a very narrow temperature range.
Bourim et al.20,21 observed that the sharp change in the shear
modulus of the first order PE-FE transition in PZT is associ-
ated with a sharp maximum in internal friction. This energy
dissipation was rationalized with the motion of domain walls,
which is suggested to be viscous in nature and affects not
only the mechanical losses but also dielectric losses.22 Later,
a slightly revised phase diagram for PZT was proposed based
on low temperature measurements of elastic moduli.23 For
the canonical relaxor PMN, it was demonstrated that the
frequency-dispersive broad maximum in permittivity is corre-
lated with a minimum in elastic stiffness and a subsequent
saturation.24 The likewise canonical relaxor PLZT 8/65/35
reveals a similar minimum in Y(T), however, well below the
maximum in the dielectric permittivity.25
a)Author to whom correspondence should be addressed. Electronic mail:
0021-8979/2014/115(8)/084108/7/$30.00 VC 2014 AIP Publishing LLC115, 084108-1
JOURNAL OF APPLIED PHYSICS 115, 084108 (2014)
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Consequently, it is appealing to employ elastic measure-
ments to clarify the underlying physical mechanisms for the
peculiar dielectric properties of lead-free BNT-based relax-
ors. Unfortunately, little is known about the elastic behavior
of these materials. For the presumably morphotropic phase
boundary (MPB) composition BNT-6BT Cordero et al.26
observed a maximum in the compliance at approximately
190 �C, which was confirmed by other authors.27 The relaxor
features of BNT-6BT, however, were not reflected in their
analysis, since BNT-6BT at the time was predominantly
assumed to be a ferroelectric transforming into an antiferro-
electric before it converts into a paraelectric cubic phase.7
Moreover, the study was limited to the pseudobinary BNT-
100xBT systems. It is currently not known whether a ternary
end-member like BZT or KNN, which are known to have
tremendous effects on the constitutive large and small signal
behavior, has a significant effect on the elastic properties.
In this work, we use the impulse excitation technique to
investigate the temperature-dependent Young’s modulus for
two unpoled lead-free compositions: BNT-20BKT and BNT-
20BKT-4BZT. The former represents a nonergodic relaxor
while the latter embodies an ergodic relaxor. The dielectric
response was measured for various frequencies and com-
pared with the elastic behavior. In order to thoroughly
discuss the structure-property relationship, temperature-
dependent high-energy X-ray diffraction measurements were
performed. To resolve the expected minute changes in sym-
metry, a high resolution detector was employed that features
a maximum resolution DQ�Q�1 of up to 2 � 10�4.
II. EXPERIMENTAL
A. Sample preparation
Within this work the primarily investigated compositions
are 0.8Bi1/2Na1/2TiO3-0.2Bi1/2K1/2TiO3 and 0.96(0.8Bi1/2
Na1/2TiO3-0.2Bi1/2K1/2TiO3)-0.04BiZn1/2Ti1/2O3, referred to
as BNT-20BKT and BNT-20BKT-4BZT, respectively. As
reference, commercially available soft ferroelectric PZT
PIC151 (PI ceramics, Lederhose, Germany) and relaxor PLZT
8/65/35 (Boston Applied Technologies, Inc., Wobum, MA,
USA) were also characterized. Polycrystalline 0.94Bi1/2Na1/2
TiO3-0.06BaTiO3 (BNT-6BT) and 0.98(0.94Bi1/2Na1/2Ti
O3-0.06BaTiO3)-0.02K0.5Na0.5NbO3 (BNT-6BT-2KNN) were
synthesized by means of a mixed oxide route. The raw pow-
ders (all Alfa Aesar GmbH, Karlsruhe, Germany) Bi2O3
(99.975% purity), Na2CO3 (99.5%), BaCO3 (99.8%), K2CO3
(99.0%), ZnO2 (99.99%), Nb2O5 (99.9%), and TiO2 (99.9%)
were weighed according to the respective stoichiometric for-
mula using a precision balance (TE214S, Sartorius AG,
G€ottingen, Germany). Subsequent mixing was performed in a
planetary mill (Pulverisette 5, Fritsch GmbH, Idar-Oberstein,
Germany) with custom-made polyamide containers and zirco-
nia milling balls (M€uhlheimer GmbH, B€arnau, Germany). The
milling was done for 24 h at 250 rpm using ethanol as milling
medium. The slurries were subsequently dried in an oven
(Memmert GmbH þ Co. KG, Schwabach, Germany) at
100 �C. After pestling, the powders were calcined in covered
alumina crucibles using a box furnace (L9/KM, Nabertherm
GmbH, Lilienthal, Germany) with a dwell time of 3 h at
temperatures of 900 �C. After another milling and drying step,
the powders were manually pressed in a custom-made steel
die. The dielectric measurements were conducted on
disc-shaped samples made from a die with a 10 mm diameter.
Bar-type samples for elastic measurements were shaped by a
die with a 4� 40 mm2 cavity. In the next step, the samples
were pressed cold-isostatically (KIP 100 E, Paul-Otto Weber
GmbH, Remshalden, Germany) and then sintered in covered
alumina crucibles for 3 h at 1150 �C with a heating rate of
5 �C/min in a box furnace (L16/14, Nabertherm GmbH,
Lilienthal, Germany). In order to minimize the evaporation of
volatile elements, the samples were partially covered in pow-
der of the respective composition. By subsequent grinding, the
sample geometry was adjusted and a surface layer of at least
200 lm was removed. Specimens for elastic measurements
had a size of approximately 3� 3� 35 mm3, while specimens
for dielectric measurements had a diameter of 7 mm and a
height of 0.7 mm.
B. Dynamic Young’s modulus
The measurement of the fundamental flexural resonance
frequency fR was performed on unpoled bar-type samples
with a cross-sectional area of 3� 3 mm2 at a resonance fre-
quency using a damping analyzer (RFDA-HT1750, IMCE,
Genk, Belgium). This technique, referred to as the impulse
excitation technique, acoustically measures the natural fre-
quency of the sample in response to a small mechanical
impulse. The Young’s modulus Y was calculated from the
resonance frequency fR by means of the following
equation:28
YðfRÞ ¼ 0:9465 � m � f 2R
b
� �� L3
t3
� �� Tl; (1)
where mass m, width b, length L, thickness t, and a correc-
tion factor Tl that accounts for the finite thickness of the bar
and the Poisson’s ratio. Since the Poisson’s ratio is not
known, the following approximation is applied:29
Tl ¼ 1þ 6:575 � t
L
� �2
: (2)
In contrast to macroscopically piezoelectric specimens, the
Young’s modulus of unpoled materials does not depend on
whether the electrodes are short-circuited or open. The reso-
nance frequency is recorded for both heating and cooling
with a maximum temperature of 700 �C and a heating and
cooling rate of 2 K�min�1.
C. Dielectric measurements
The temperature-dependent dielectric behavior of
unpoled specimens was measured with an impedance ana-
lyzer (HP4284A, Hewlett Packard Japan, LTD., Kobe,
Japan). The custom-built sample holder consisted of a plati-
num top and bottom electrode and was placed into a box fur-
nace (LE4/11/R6, Nabertherm GmbH, Lilienthal, Germany).
Using a ramp of 2 K�min�1, the permittivity was measured
for temperatures up to 400 �C at the frequencies of 0.1 kHz,
084108-2 Dittmer et al. J. Appl. Phys. 115, 084108 (2014)
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1 kHz, 10 kHz, 100 kHz, and 1000 kHz with a measurement
amplitude of 1 V. A LabVIEW program was used for
data-acquisition by means of an analog-digital-converter (TI
GPIB-USB-HS, Texas Instruments, Inc., Dallas, TX, USA).
D. High-temperature X-ray diffraction
The high-temperature XRD measurements were per-
formed at the 11BM-B beamline at the Advanced Photon
Source (APS) within the Argonne National Laboratory
(Lemont, IL, USA). Disc-shaped ceramic samples of compo-
sitions BNT-20BKT and BNT-20BKT-4BZT were ground
using a mortar and pestle and annealed for 30 min at 400 �C.
The powder was loosely filled into a quartz capillary with a
diameter of 0.7 mm, which was then mounted into a goniom-
eter head for alignment and spun with>90 Hz. Placed into
the high-energy, monochromatic X-ray beam with a wave-
length of 0.0458739 nm, the diffraction patterns were col-
lected from 0.5�< 2h< 38�. The detector is a multi-analyzer
array consisting of 12 independent Si(111) crystal analyzers
and LaCl3 scintillation detectors allowing for high resolu-
tions of approximately DQ/Q � 2 � 10�4 with Q being the
scattering angle. Temperature control was realized by means
of a hot gas blower (Cyberstar, Echirolles, France).
Diffraction patterns with a collection time of 2 min were
recorded consecutively during increasing temperature with a
heating ramp of 5 K�min�1 to 350 �C. The step width was
h¼ 0.002�.
III. RESULTS
The dynamic Young’s modulus Y is presented in Fig. 1
as a function of temperature for unpoled BNT-20BKT and
BNT-20BKT-4BZT. Both compositions show a strongly
nonlinear temperature-dependent Young’s modulus. At room
temperature BNT-20BKT exhibits a Y of 100 GPa, decreas-
ing upon heating down to a minimum of 91 GPa in the range
of 100 �C–200 �C. Higher temperatures cause a stiffening of
the sample; the Young’s modulus increases and eventually
shows a saturation behavior at approximately 127 GPa at
700 �C. BNT-20BKT-4BZT demonstrates the same behavior
yet with a slightly higher Y at both room temperature
(112 GPa) and 700 �C (135 GPa) with a minimum of
101 GPa. There is virtually no difference in the heating and
the cooling curve of both compositions, that is, there is no
apparent thermal hysteresis within the resolution of the
measurements.
BNT-6BT and BNT-6BT-2KNN exhibit an equivalent
thermal evolution of Y as demonstrated by Fig. 2. In addi-
tion, the unpoled lead-containing compounds PZT and PLZT
likewise display a significant increase in Y. For PZT, the
Young’s modulus increases by 153% from 66 GPa at 25 �Cto 167 GPa at 450 �C while for PLZT the Young’s modulus
increases by 67% from 98 GPa at room temperature to
164 GPa at 450 �C.
The dielectric response of both BNT-BKT-based materi-
als displays two notable features. In a low-temperature
FIG. 1. Young’s modulus and dielectric
properties for (a) and (c) BNT-20BKT
and (b) and (d) BNT-20BKT-4BZT (b)
and (d).
FIG. 2. Young’s modulus in addition
to permittivity and loss tangent for (a)
and (e) BNT-6BT, (b) and (f) BNT-
6BT-2KNN, (c) and (g) soft PZT, and
(d) and (h) PLZT 8/65/35.
084108-3 Dittmer et al. J. Appl. Phys. 115, 084108 (2014)
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region up to approximately 200 �C, there is a frequency-
dispersive shoulder in er, i.e., higher frequencies cause a
decrease in permittivity. The loss factor is likewise
frequency-dependent as higher frequencies give rise to an
increase in dielectric losses. This behavior is qualitatively
the same for both compositions; however, the shoulder is
slightly more pronounced for BNT-20BKT. At higher tem-
peratures, the dispersion decreases and a maximum in er(T)
emerges at a temperature Tm¼ 327 �C in BNT-20BKT and
Tm¼ 321 �C in BNT-20BKT-4BZT. The corresponding peak
permittivity at 100 Hz decreases by 5% from 4128 to 3917.
Closer inspection reveals that this maximum also involves
frequency dispersion, albeit minute, at the high-temperature
side of the peak. Interestingly, a higher measurement fre-
quency yields a higher permittivity and also higher losses,
which is in contrast to the low-temperature shoulder where
higher frequency f causes a decrease in tand.
Close inspection of the individual diffraction patterns at
room temperature confirms a pseudocubic structure for both
compositions (Fig. 3). Upon temperature increase, the shape
of the reflections remains largely unchanged while shifting
to lower 2h values. This shift is caused by thermal expansion
and visualized in detail for the {111}pc (where the subscript
“pc” denotes pseudocubic indices) reflection in Fig. 4. The
most striking difference between both compositions is the
full width at half maximum (FWHM), which is notably
higher for BNT-20BKT.
IV. DISCUSSION
The frequency dispersion observed in the dielectric
measurements can be ascribed to the presence of PNRs and
their dynamics.17 The size distribution of these PNRs gives
rise to a broad distribution of relaxation times. Thus, the
measured permittivity depends on the probing frequency. At
higher frequencies large, PNRs are too slow to follow
the excitation field and, consequently, the permittivity
decreases while the loss factor increases. In general, heating
of a relaxor causes the shrinkage of PNRs.17 The permitti-
vity response increases because the “active” fraction of
PNRs that may follow the external field increases. In the
canonical lead-containing relaxors further heating reduces
the overall volume fraction of PNRs; thus, the er eventually
peaks at a frequency-dependent temperature Tm beyond
which the permittivity response declines. In BNT-based
relaxors, however, the frequency dispersion almost vanishes
approximately at 100 �C that is below the maximum
permittivity.
In perovskites, a peak in permittivity often denotes
a phase transition. In the case of the currently studied
FIG. 3. Temperature-dependent dif-
fraction patterns for (a) BNT-20BKT
and (b) BNT-20BKT-4BZT from room
temperature to 350 �C.
FIG. 4. Contour plot of the {111}pc
reflection as a function of temperature
for (a) BNT-20BKT and (b)
BNT-20BKT-4BZT from room tem-
perature up to 350 �C.
084108-4 Dittmer et al. J. Appl. Phys. 115, 084108 (2014)
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BNT-based ceramics, however, the diffraction patterns
appear pseudocubic and there is no evidence for a
temperature-driven phase transition. The observed changes
can be attributed to thermal expansion. The {111}pc reflec-
tion was fit to a pseudo-Voigt function to determine the peak
position and the FWHM as a function of temperature.
According to Fig. 5, the coefficient of thermal expansion is
very similar for both compositions. Linear fitting yields for
the {111}pc reflection a shift of 9.7 � 10�5 K�1 for
BNT-20BKT and 10.3 � 10�5 K�1 for BNT-20BKT-4BZT.
The FWHM found for BNT-20BKT is 12 � 10�3 (deg.) for
the {111}pc reflection compared to around 7.5 � 10�3 (deg.)
for the corresponding reflection in BNT-20BKT-4BZT.
Across the investigated temperature range, the FWHM of
both compositions is nearly invariant. Therefore, the diffrac-
tion experiments do not reveal any symmetry breaking with
increasing temperature. Structural phase transitions are typi-
cally observed when the symmetry decreases due to splitting
in characteristics peaks, e.g., {111}pc in rhombohedral or
{200}pc in tetragonal symmetry. In the present work, a subtle
distortion that may be present at low temperature may be
measured in a broader FWHM. If a phase transition occurs
with increasing temperature, a decrease in the FWHM might
be expected. In the present results, little change in FWHM
was detected across the entire measured temperature range.
Thus, it can be concluded that the effects contributing to the
dielectric and elastic behaviors are of a length below the co-
herence length for X-ray diffraction. For example, the canon-
ical relaxor PMN remains pseudocubic from �268 �C to
620 �C,30 while similar results have been reported also for
Pb(Mg1/3Ta2/3)O3.31 In addition, high-temperature diffrac-
tion measurements reported for related lead-free BNT-based
materials comply with the currently observed temperature
invariance of the structure.32–34
In contrast to the XRD patterns, the Young’s modulus
changes significantly with temperature. In many ceramics,
such as alumina35 or magnesia,36 the Young’s modulus
decreases linearly with temperature as long as structural
phase transformations are absent. This observation is gener-
ally explained by the decreasing strength of bonds with tem-
perature, that is, the slope of the asymmetric interatomic
potential curve decreases with temperature.37 It was pro-
posed by Wachtman et al.38 that the Young’s modulus in
oxides actually displays exponential temperature dependence
in the form of
YðTÞ ¼ Y0K � A � T � expð�T0=TÞ; (3)
where the Young’s modulus Y0K at absolute zero temperature
and the constants T0 and A. For high temperatures, the term
exp(�T0/T) approaches unity and, therefore, a linear depend-
ence is observed at room temperature and beyond. A devia-
tion from this general behavior is observed when a material
undergoes structural changes such as phase transition,39 glass
transition,40 or changes in the microstructure41 due to the
appearance or closure of microcracking or changes in grain
boundary characteristics. Within the context of ferroelectric
materials, a significant softening is expected when a parae-
lastic-to-ferroelastic transition takes place, which is usually
at the Curie point Tc, due to the formation of ferroelastic
domains.42 It follows that an unusual softening leading to a
negative deviation from the usual linear decrease with
increasing temperature can happen when ferroelastic transi-
tion occurs. In the case of the ferroelastic transition, the
Young’s modulus is expected to establish a local minimum
around the transition point due to the multiplication of
equally stable orientations of coexisting symmetries.
The observed profiles of the temperature-dependent
Young’s modulus plot shown in Fig. 1 are untypical in that
they show two distinctive anomalies. One is a diffuse local
minimum in the temperature range at approximately 150 �C,
and the other is an increase of Young’s modulus asymptoti-
cally to a saturation behavior. By contrast, no such minimum
is found in PZT. Instead, the Young’s modulus is virtually
constant up to about 230 �C and subsequently increases
sharply with a maximum slope at 234 �C (Figure 2(c)). This
abrupt change denotes a ferroelastic-to-paraelastic (or equiva-
lently ferroelectric-to-paraelectric in this case) phase transi-
tion, which is also reflected in the dielectric constant peaking
at about 250 �C. The same principle trend is reported not only
for PZT21 but also for Mn-doped PMN-PT,43,44 where the
FE-PE transition at 170 �C complies with a peak in permittiv-
ity.43,44 As demonstrated by Fig. 6, the maximum in e(T) is
shifted for PLZT as compared to PZT. In agreement with ear-
lier reports,45 not only the temperature of maximum permit-
tivity Tm is lowered but also the transition spans a broader
temperature range than in PZT.46 This broadening effect was
rationalized with the disruption of long-range order, i.e., the
formation of PNRs and their reduction in size with increasing
lanthanum content.47 In other words, the conversion of fer-
roelastic PNRs into paraelastic cubic matrix takes place over
a wide range of temperature. The temperature-dependent
Young’s modulus likewise reveals a broadening. This means
that the relaxor nature is indeed reflected in the
temperature-dependence of the Young’s modulus.
FIG. 5. Reflection angle 2h and
FWHM of the {111}pc reflection deter-
mined for (a) BNT-20BKT and (b)
BNT-20BKT-4BZT from room tem-
perature to 350 �C.
084108-5 Dittmer et al. J. Appl. Phys. 115, 084108 (2014)
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The comparison with PLZT suggests that the tempera-
ture dependent Young’s modulus above 200 �C is due to a
gradual conversion of ferroelastic PNRs into paraelastic
cubic matrix, while the presence of a local minimum in the
Young’s modulus below 200 �C in BNT-based relaxors can
be best-explained by assuming a diffuse ferroelastic phase
transition of PNRs.7 In order to quantify the interval width
where most changes in Y occur, tangents are constructed for
the initial linear region, the intermediate linear region, and
the final saturated region. The intersection of the former
two yields Tonset,1, a measure for the temperature of the
minimum Young’s modulus. The intersection of the latter
two tangents provides Tonset,2, which affords an estimation
of the onset of saturation. Both values are listed for all
investigated materials in Table I. BNT-20BKT has a Tonset,1
of 98 6 5 �C and a Tonset,2 of 493 6 5 �C. The addition of
4 mol. % BZT causes a shift of both temperatures to
Tonset,1¼ 96 6 5 �C and Tonset,2¼ 535 6 5 �C. It must be
noted that Feile et al.48 found a correlation between the
minimum in Y(T) and the freezing temperature of single
crystals of the solid solution (KBr)1�x(KCN)x, a dipole
glass system. In the presently investigated lead-free sys-
tems, by contrast, the minimum in Y(T) is largely invariant
on composition while freezing shifts to notably lower tem-
peratures. The interval DT between both onset temperatures
is broad at 395 6 5 �C for BNT-20BKT and 439 6 5 �C for
BNT-20BKT-4BZT. This general progression is also in
good agreement with the relaxor PMN as measured by
ultrasound49 and Brillouin light scattering,50 where
Young’s modulus (C11) was found to vary likewise across
hundreds of degrees centigrade.
It is noted that the onset of the saturation behavior is
near the Curie point TC of PZT and Burns temperature TB of
PLZT, both of which are located near �300 �C. By analogy,
it is suggested that TB of the studied BNT-based relaxors can
be estimated from the onset of the saturation behavior at
�700 �C, consistent with the previous studies.7,51
Consequently, it is suggested that measuring Y(T) up to
900 �C or 1000 �C and comparing with dielectric and TEM
measurements could be useful in verifying if TB can be deter-
mined from elastic measurements. Such a high-temperature
approach, however, is not trivial and is thus reserved for
future investigations.
Another important observation is the increase in room
temperature stiffness with incorporation of BZT, which can
be rationalized by two potential mechanisms. First, the stiff-
ening may be induced by the chemical modification with the
heterovalent zinc ions. Similar effects are well-known for
metals, where solid solution hardening is employed to
increase strength and hardness but also the Young’s modu-
lus.52 The effect of solid solution hardening is also known
for both structural53 and functional ceramics, for example,
iron doping of PZT increases the elastic stiffness.54
Second, the BZT modification increases the volume
fraction of the metrically cubic phase at the expense of the
non-cubically distorted PNRs. The high-temperature cubic
phase of PZT21 and PLZT,25 in addition to other perovskites
such as ST42 or BT,19 displays a higher Young’s modulus
than the respective low-temperature phases of lower symme-
try. Judging from unit cell parameters reported for BT, the
FE-PE transition is not coupled to an increase in unit cell
size.55 Therefore, the higher Y of the cubic phase is not
caused by a higher packing density but is probably related to
the higher symmetry. Accordingly, an increase in volume
fraction of the pseudocubic phase may cause an increase in
Young’s modulus. As stated in Table I, the effect of
enhanced Young’s modulus by chemical modification is
observed also for the BNT-6BT-100yKNN system, where
2 mol. % KNN increase Y from 103 GPa to 111 GPa. It is
apparent from Figs. 1 and 2 that the modified compositions
display higher elastic moduli throughout the whole tempera-
ture range.
V. CONCLUSIONS
In conclusion, measurement of the resonance frequency
afforded a detection of changes in the local structure caused
by the thermal evolution of PNRs. These structural changes
are not evidenced in high-resolution X-ray diffraction due to
the small length scale of the effect. It was suggested that a
minimum in the temperature-dependent Young’s modulus
should be the result of a diffuse ferroelastic phase transition.
In addition, it was found that the modification with a ternary
end-member resulted in an increases in the Young’s
modulus.
FIG. 6. Comparison of PLZT, PZT, 20BKT, and 4BZT in terms of reso-
nance frequency and relative dielectric permittivity normalized to their re-
spective room temperature value.
TABLE I. Onset-temperatures Tonset1 and Tonset2, temperature interval of
transition DT, room temperature Young’s modulus Y25 �C, and maximum rel-
ative deviation DY from room temperature Young’s modulus. Note that all
temperatures are estimated to have a maximum error of 65 �C.
Composition Tonset1/ �C Tonset2/ �C DT/ �C Y25 �C/GPa DY/%
BNT-19BKT-0BZT 98 493 395 100 11.9
BNT-19BKT-4BZT 96 535 439 112 9.8
BNT-6BT 114 488 374 103 12.1
BNT-6BT-2KNN 90 509 419 111 11.2
PZT 228 295 67 66 54.2
PLZT 68 216 148 99 29.2
084108-6 Dittmer et al. J. Appl. Phys. 115, 084108 (2014)
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ACKNOWLEDGMENTS
This work was financially supported by the Deutsche
Forschungsgemeinschaft (DFG) under SFB595/A1. Use of
the Advanced Photon Source, an Office of Science User
Facility operated for the U.S. Department of Energy (DOE)
Office of Science by Argonne National Laboratory, was
supported by the U.S. DOE under Contract No. DE-AC02-
06CH11357. We would like to acknowledge Dr. Matthew
Suchomel for technical assistance and useful discussion.
K.G.W. acknowledges support by the Deutsche
Forschungsgemeinschaft under WE 4972/1-1. J.L.J.
acknowledges the U.S. Department of the Army under
W911NF-09-1-0435 for enabling his contributions.
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